Lectures related to Hamiltonian dynamics on convex polytopes

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.

Covers the KKT conditions and convex optimization, discussing constraint qualifications and tangent cones of convex sets.

Covers cyclically monotone sets in optimal transport theory and their properties.

Covers the concept of convex functions and their applications in optimization problems.

Explores convex functions, global minima, and their relationship with differentiability.

Explores convex sets, their properties, and applications in optimization.

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Explores Lagrange multipliers, minimax theorems, and convex subsets in optimal transport theory.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores optimal transport, emphasizing convexity properties and inequalities in compact sets.

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores convex sets, Minkowski-Weyl theorem, and Separation theorem in convex analysis.

Explores the Closest Vector Problem and Voronoi cells in lattice reduction algorithms.

Explores fields deriving from a potential, emphasizing integral and linear aspects.

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Explores optimal transport and gradient flows in Rd, emphasizing convergence and the role of Lipschitz and Picard-Lindelöf theorems.